State-space models formalize the probabilistic description of a
time-dependent latent process—the state—observed indirectly at
discrete times [1]}. These models can approximate a
wide variety of stochastic processes, ranging from the evolution of
atmospheric variables in meteorology to the volatility of financial
assets. This paper is concerned with the problem of (discrete-time)
filtering, i.e., characterizing the sequence of conditional
distributions of the latent field at observation times, given all
available measurements up to that time. Filtering arises in virtually
every discipline that seeks an online integration of models
with data, e.g., imaging, pharmacology, atmospheric sciences, and
oceanography. In geophysical applications, filtering and several
closely related inference problems (e.g., smoothing, sequential
parameter inference) fall under the broad label of data
assimilation.
